module Meas12 () where

import Language.Haskell.Liquid.Prelude

mylen          :: [a] -> Int
mylen []       = 0
mylen (_:xs)   = 1 + mylen xs


mymap f []     = []
mymap f (x:xs) = (f x) : (mymap f xs)

myreverse = go []
  where go acc (x:xs) = go (x:acc) xs
        go acc []     = acc
    
myapp [] ys     = ys
myapp (x:xs) ys = x:(myapp xs ys)

zs :: [Int]
zs = [1..100]

zs' :: [Int]
zs' = [500..1000]

prop2 = liquidAssertB (n1 == n2) 
  where n1 = mylen zs
        n2 = mylen $ mymap (+ 1) zs 

prop3 = liquidAssertB (n1 == n2) 
  where n1 = mylen zs
        n2 = mylen $ myreverse zs 

prop4 = liquidAssertB ((n1 + n2) == n3) 
  where n1 = mylen zs
        n2 = mylen zs'
        n3 = mylen $ myapp zs zs' 

prop5 = zipWith (+) zs (0: myreverse zs)
